The authors sought to test Homans' proposition that small groups inevitably generate a social structure which combines subgroups (cliques) and a ranking system. We present a graph theoretical model of such a structure and prove that a necessary and sufficient condition for its existence is the absence of seven particular triad types. Expected frequencies of the seven triad types in random graphs are deduced from elementary probability theory, and we suggest that a reasonable operational statement of Homans' theory is that in most groups, the seven key triads are less frequent than the random model would predict. A data pool of sociograms and sociomatrices from 427 groups was collected from diverse published and unpublished studies. Random samples of 30 school and 30 adult groups were drawn from the pool and analysed. Significant majorities of both samples showed deviations from chance in the directions predicted. As a check, 60 simulated groups with truly random relationships were analysed and found to be close to the chance expectations and quite different from the real data samples. Overall, we claim support for Homans' theory. (Author)